The success of machine-learned potentials used in combination with MD simulations
has been demonstrated in a variety of applications, from the study of phase
transitions in halide perovskites [1]} and lithium manganese
oxide spinels [2]} to thermal conductivities in solid and amorphous
silicon [3]} and the CoSb\(_3\)  skutterudite [4]}.
For any MLFF, however, it is extremely
challenging to simultaneously describe vibrational properties, dynamical changes
of lattice parameters during phase transitions, and anharmonic effects relevant
for transition temperatures as well as thermal conductivity. In fact, none of
Refs. [1]}, [2]}, [3]}, [4]} show the ability
of MLFFs to describe all these different thermodynamic properties simultaneously.
Harmonic vibrational properties are already a stringent test of the quality of ML
potentials, especially when considering materials with soft phonon modes and
different polymorphs [9]}. However, the description of phonon
dispersion relations requires the acquisition of only a two-body term, the
harmonic force constants. Anharmonicity, on the other hand, requires the
development of a surrogate model for tiny, subtle energy differences on the
highly corrugated harmonic energy surface. The MLFF must capture at least
third-order anharmonic force constants, the coupling between phonons and
lattice distortions, and, especially at high temperature, even higher-order
anharmonic force constants. For example, calculating just the third-order terms easily requires more than
a thousand first-principles calculations.
Whether machine-learned potentials can describe all these effects with
satisfactory accuracy has been insufficiently investigated.
